Algorithm For Constrained Optimization Problems Research Articles

An Improved Genetic Algorithm for Constrained Optimization Problems

The mathematical form of many optimization problems in engineering is constrained optimization problems. In this paper, an improved genetic algorithm based on two-direction crossover and grouped mutation is proposed to solve constrained optimization problems. In addition to making full use of the direction information of the parent individual, the two-direction crossover adds an additional search direction and finally searches in the better direction of the two directions, which improves the search efficiency. The grouped mutation divides the population into two groups and uses mutation operators with different properties for each group to give full play to the characteristics of these mutation operators and improve the search efficiency. In experiments on the IEEE CEC 2017 competition on constrained real-parameter optimization and ten real-world constrained optimization problems, the proposed algorithm outperforms other state-of-the-art algorithms. Finally, the proposed algorithm is used to optimize a single-stage cylindrical gear reducer.

Parallelized Multiple Swarm Artificial Bee Colony (PMS-ABC) Algorithm for Constrained Optimization Problems

Parallelized Multiple Swarm Artificial Bee Colony (PMS-ABC) Algorithm for Constrained Optimization Problems

A Hybrid Cultural Harmony Search Algorithm for Constrained Optimization Problem of Diesel Blending

This paper studies the constrained optimization problem for nonlinear diesel blending. A new hybrid algorithm called cultural harmony search algorithm is presented to solve the proposed optimization problem, which uses cultural knowledge in the belief space of the cultural algorithm to guide the evolving and searching process of the harmony search algorithm. Then, an improved harmony improvisation in the population space of cultural algorithm is developed for new harmony generation to enrich the population diversity. Moreover, in order to accelerate convergence, the domain of decision variables is scaled down by a simplex method at the beginning of the algorithm, and a simplex improved cultural harmony search algorithm is provided. Finally, benchmark functions and the results of application in nonlinear diesel blending of a real-world refinery show the feasibility and effectiveness of the proposed algorithms. The contrasted experiments show that our proposed hybrid algorithm is better than other hybrid algorithms, especially in diesel blending optimization problem.

Constraint Consensus Based Artificial Bee Colony Algorithm for Constrained Optimization Problems

Over the last few decades, evolutionary algorithms (EAs) have been widely adopted to solve complex optimization problems. However, EAs are powerless to challenge the constrained optimization problems (COPs) because they do not directly act to reduce constraint violations of constrained problems. In this paper, the robustly global optimization advantage of artificial bee colony (ABC) algorithm and the stably minor calculation characteristic of constraint consensus (CC) strategy for COPs are integrated into a novel hybrid heuristic algorithm, named ABCCC. CC strategy is fairly effective to rapidly reduce the constraint violations during the evolutionary search process. The performance of the proposed ABCCC is verified by a set of constrained benchmark problems comparing with two state-of-the-art CC-based EAs, including particle swarm optimization based on CC (PSOCC) and differential evolution based on CC (DECC). Experimental results demonstrate the promising performance of the proposed algorithm, in terms of both optimization quality and convergence speed.

PSO+: A new particle swarm optimization algorithm for constrained problems

The Particle Swarm Optimization algorithm is a metaheuristic based on populations of individuals in which solution candidates evolve through simulation of a simplified model of social adaptation. By aggregating robustness, efficiency and simplicity, PSO has gained great popularity. Modified PSO algorithms have been proposed to solve optimization problems with domain, linear and nonlinear constraints. Other algorithms that use multi-objective optimization to deal with constrained problems face the problem of not being able to guarantee finding feasible solutions. Current PSO algorithms that deal with constraints only treat domain constraints by controlling the velocity of particle displacement in the swarm, or do so inefficiently by randomly resetting each infeasible particle. This approach may make it infeasible to optimize certain problems, especially real ones. This work presents a new particle swarm optimization algorithm, called PSO+, capable of solving problems with linear and nonlinear constraints in order to solve these deficiencies. The proposed algorithm uses a feasibility repair operator and two swarms to ensure there will always be a swarm whose particles fully respect every constraint. A new particle update method is also proposed to insert diversity into the swarm and improve search-space coverage, allowing the search-space border to be exploited as well, which is particularly convenient when the optimization involves active constraints in global optimum. Two heuristics are proposed to initialize a feasible swarm with the purpose of speeding up the initialization mechanism and ensuring diversity at the starting point of the optimization process. Furthermore, a neighborhood topology is proposed to minimize premature convergence. The proposed algorithm was tested for twenty-four benchmark functions, as well as in a real reservoir drainage plan optimization problem. Results attest that the new algorithm is competitive, since it increases the efficiency of the PSO and the speed of convergence.

Troop search optimization algorithm for constrained problems

Troop search optimization (TSO) algorithm is motivated by the dynamic controls of commander/captain over the troops before (during) each combat operation to concoct (active) a bravery battalion force. The attempt is focused to maintain the proper balance between exploration and exploitation in the search space during simulation. The inclusion of operators like ‘swapping crossover’ and ‘cut and fill’ provides additional features in TSO algorithm to make it more robust. The efficiency of TSO is tested over a set of constrained optimization problem test suite CEC 2010. Apart from that, TSO is also employed to solve five real life constrained engineering optimization problems. The empirical results, comparative statistical and graphical analysis concludes with the superiority of TSO over the state-of-art algorithms in solving constrained optimization problems.

Hybrid Immune Clonal Particle Swarm Optimization Multi-Objective Algorithm for Constrained Optimization Problems

How to solve constrained optimization problems constitutes an important part of the research on optimization problems. In this paper, a hybrid immune clonal particle swarm optimization multi-objective algorithm is proposed to solve constrained optimization problems. In the proposed algorithm, the population is first initialized with the theory of good point set. Then, differential evolution is adopted to improve the local optimal solution of each particle, with immune clonal strategy incorporated to improve each particle. As a final step, sub-swarm is used to enhance the position and velocity of individual particle. The new algorithm has been tested on 24 standard test functions and three engineering optimization problems, whose results show that the new algorithm has good performance in both robustness and convergence.

An Adaptive Hybrid PSO Multi-Objective Optimization Algorithm for Constrained Optimization Problems

In attempting to overcome the limitation of current methods to solve complicated constrained optimization problems, this paper proposes an adaptive hybrid particle swarm optimization multi-objective optimization (AHPSOMO) algorithm. In the early stage, this algorithm initializes the individuals in a population in an even manner using good point set (GPS) theory so that the diversity of the population can be guaranteed. In the process of local search, differential evolution (DE) algorithm is introduced for updating local optimal individuals. Particle swarm optimization method is further adopted to conduct global search as per the multi-objective approach. The results of simulation tests on 24 classic test functions and three engineering constrained optimization problems show that compared with other algorithms, our proposed algorithm is effective and feasible, which can offer highly accurate solutions with good robustness.

An improved artificial bee colony algorithm for solving constrained optimization problems

The artificial bee colony (ABC) algorithm is a global stochastic optimization algorithm inspired by simulating the foraging behavior of honey bees. It has been successfully applied to solve the constrained optimization problems (COPs) with a constraint handling technique (Deb’s rules). However, it may also lead to premature convergence. In order to improve this problem, we propose an improved artificial bee colony (I-ABC) algorithm for COPs. In I-ABC algorithm, we firstly relax the Deb’s rules by introducing the approximate feasible solutions to suitably utilize the information of the infeasible solutions with better objective function value and small violation. Next, we construct a selection strategy based on rank selection and design a search mechanism using the information of the best-so-far solution to balance the exploration and the exploitation at different stages. In addition, periodic boundary handling mode is used to repair invalid solutions. To verify the performance of I-ABC algorithm, 24 benchmark problems are employed and two comparison experiments have been carried out. The numerical results show that the proposed I-ABC algorithm has an outstanding performance for the COPs.

Particle Swarm Optimization-based Augmented Lagrangian Algorithm for Constrained Optimization Problems

Particle Swarm Optimization-based Augmented Lagrangian Algorithm for Constrained Optimization Problems

A Hybrid Genetic Algorithm for Constrained Optimization Problems

Abstract —Genetic algorithm (GA) is a powerful method to solve constrained optimization problems (COPs). In this paper, a new fitness function based hybrid genetic optimization algorithm (NFFHGA) for COPs is proposed, in which a new crossover operator based on Union Design is presented, and inspired by the smooth function technique, a new fitness function is designed to automatically search for potential solutions. Furthermore, in order to make the fitness function work well, a special technique which keeps a certain number of feasible solutions is also used. Experiments on 6 benchmark problems are performed and the compared results with the best known solutions reported in literature show that NFFHGA can not only quickly converge to the optimal or near-optimal solutions, but also have a high performance.

<I>e</I>-Differential Evolution Algorithm for Constrained Optimization Problems

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A Novel Improved Differential Evolution Algorithm for Constrained Optimization Problems

A Novel Improved Differential Evolution Algorithm for Constrained Optimization Problems

A Constraints Scattered Memetic Algorithm for Constrained Optimization Problem

In this paper, a constraints scattered memetic algorithm (CSMA), which integrates a novel constraints scattered genetic algorithm (CSGA) and the traditional interior point method, is proposed for solving constrained optimization problems. In CSGA, a constraint scattering operation, a sub-population crossover method and a new population performance evaluation mechanism are employed. The complete constraints of a problem are divided into several sub-populations and all these sub-populations are crossed after their respective evolution process. In this way, the difficulty of obtaining feasible individuals in many strong constrained conditions is well overcome. And according to the newly defined population performance index, individuals with larger population diversity are chosen for further local search. These new mechanisms are combined in CSGA and interior point method is further employed as a local search operator for exploitation. Experiments and comparisons over a set of standard test functions show that population with better performance can be generated during the iteration of CSGA and the proposed CSMA has a better solution precision at less computation cost than most of the other algorithms reported in literature.

A New Differential Evolution Algorithm for Constrained Optimization Problem

A New Differential Evolution Algorithm for Constrained Optimization Problem

Particle swarm optimization algorithm for constrained problems

AbstractA novel particle swarm optimization (PSO) algorithm with the evaluation of infeasibility degree (IFD) of constraints is presented for nonlinear programming (NLP) problems with equality and inequality constraints. The IFD of constraints is defined as the sum of the squared values of the constraint violations. The proposed novel PSO updates the local best position and global best position according to the objective value and the value of IFD simultaneously. The results of several numerical tests and one real engineering optimization problem show that the proposed approach is efficient. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd.

A Runtime Analysis of Evolutionary Algorithms for Constrained Optimization Problems

Although there are many evolutionary algorithms (EAs) for solving constrained optimization problems, there are few rigorous theoretical analyses. This paper presents a time complexity analysis of EAs for solving constrained optimization. It is shown when the penalty coefficient is chosen properly, direct comparison between pairs of solutions using penalty fitness function is equivalent to that using the criteria ldquosuperiority of feasible pointrdquo or ldquosuperiority of objective function value.rdquo This paper analyzes the role of penalty coefficients in EAs in terms of time complexity. The results show that in some examples, EAs benefit greatly from higher penalty coefficients, while in other examples, EAs benefit from lower penalty coefficients. This paper also investigates the runtime of EAs for solving the 0-1 knapsack problem and the results indicate that the mean first hitting times ranges from a polynomial-time to an exponential time when different penalty coefficients are used.

Improved dual algorithm for constrained optimization problems

One class of effective methods for the optimization problem with inequality constraints are to transform the problem to a unconstrained optimization problem by constructing a smooth potential function. In this paper, we modifies a dual algorithm for constrained optimization problems and establishes a corresponding improved dual algorithm; It is proved that the improved dual algorithm has the local Q-superlinear convergence; Finally, we performed numerical experimentation using the improved dual algorithm for many constrained optimization problems, the numerical results are reported to show that it is valid in practical computation.

Stochastic Approximation Algorithms for Constrained Optimization Problems

The paper gives convergence theorems for several sequential Monte-Carlo or stochastic approximation algorithms for finding a local minimum of a function $f(\bullet)$ on a set $C$ defined by $C = \{x: q^i(x) \leqq 0, i = 1, 2, \cdots, s\}. f(\bullet)$ is unknown, but noise perturbed values can be observed at any desired parameter $x \in C$. The algorithms generate a sequence of random variables $\{X_n\}$ such that (for a.a. $\omega$) any convergent subsequence of $\{X_n(\omega)\}$ converges to a point where a certain necessary condition for constrained optimality holds. The techniques are drawn from both stochastic approximation, and non-linear programming.